Chemistry 457 - Homework #7 Solution
due: Friday, May 16th at 5:00 pm
Readings: Chapter 16 in Engel & Reid. Students may also want to review multidimensional
integration in both Cartesian and spherical-polar coordinates. N.b., much of the kinetic theory o
Chemistry 457 - Homework #4 Solution
due: Friday, April 25th at 5:00 pm
Problem 1 - Relative Boltzmann Distribution. Using the relative Boltzmann distribution
ni () = nk () exp([i k ])
determine the temperature T = (k)1 at which the population of the fth
Chemistry 457 - Homework #5 Solution
due: Friday, May 2nd at 5:00 pm
Readings: Chapter 15 in Engel & Reid.
Problem 1 - The Einstein Solid. The vibrational partition function for the two-dimensional
Einstein solid is given by
xy
y
x
qV () = qV () qV () =
e
Chemistry 457 - Homework #9 Solution
due by 5:00pm on May 30th
Problem 1 - Vapor Pressure at Equilibrium. Suppose that radical atoms B are
condensed into a solid that can be considered as a three-dimensional Einstein crystal. Each
atom has mass mB , an is
Chemistry 452/456
End- of-term Examination Key
19 August 2005
Professor G. Drobny
Enter your answers into a blue or green Composition Book. Perform only the
number of problems required.
Useful Constants and Conversions
Universal Gas Constant= R = 8.31J /
Chemistry 452/456
End- of-term Examination Key
19 August 2011
Professor G. Drobny
Enter your answers into a blue or green Composition Book. Perform only the
number of problems required. Where needed you may enter a graph directly
into your blue book or yo
Chemistry 452/456
End- of-term Examination Key
20 August 2010
Professor G. Drobny
Enter your answers into a blue or green Composition Book. Perform only the
number of problems required. Where needed you may enter a graph directly
into your blue book or yo
Chem 455 Fall 2012 Homework 10 due Wed Dec 5 5:00pm (in box 65 on 3rd floor)
1. MO energies. Compute the energies of the two molecular orbitals of H2+ generated by combining two
hydrogen 1s AOs and carry out the calculation for
, 0.200 and 0.500 to mimic
Chem 455 Fall 2012 Homework 9 due Mon Nov 26 5:00pm (in box 65 on 3rd floor)
1. Multi-electron system. Show that the sum of the charge densities of the three singly occupied
orbitals in a half-filled p shell with electron configuration (np-1)1(np0)1(np+1)
Chem 455 Fall 2012 Homework 8 due Mon Nov 19 5:00pm (in box 65 on 3rd floor)
1. Hydrogen atom. For the 3px wavefunction of the hydrogen atom, determine the positions of the
radial and angular nodes.
The 3px wavefunction is
(
)
()(
(
)
. Nodes correspond t
Chem 455 Fall 2012 Homework 7 due Fri Nov 9 5:00pm (in box 65 on 3rd floor)
1. Angular momentum. Using the definitions of the operators , and in Cartesian coordinates,
compute the commutator [ ].
For this type of operator calculations, it helps to imagine
Chemistry 452/456
End- of-term Examination Key
23 August 2013
Professor G. Drobny
Enter your answers into a blue or green Composition Book. Perform only the
number of problems required. Where needed you may enter a graph directly
into your blue book or yo
Chemistry 452/456
End- of-term Examination
17 August 2012
Professor G. Drobny
Enter your answers into a blue or green Composition Book. Perform only the
number of problems required. Where needed you may enter a graph directly
into your blue book or you ma
Chemistry 452/456
End- of-term Examination
20 August 2014
Professor G. Drobny
Enter your answers into a blue or green Composition Book. Perform only the number of
problems required. Answers must be given in energy mass units of kilograms (kg), distance
as
Chemistry 452/456 Midterm Examination
July 22, 2013
Enter Name, student ID, course (452 or 456) and answers in a Blue Book
Useful Constants:
1 Newton=1 N= 1 kg m s-2
1 Joule=1J=1 N m=1 kgm2/s2
1 Pascal=1Pa=1N m-2
1atm=101325 Pa
1L=0.001m3
-1
-1
Univ
Chemistry 452/456
Midterm Examination
26 July , 2002
Professor G. Drobny
Part 1: (18 points) Define or explain three out of the 6 terms
a) Carnot cycle. Define and give an important result of this cycle.
Answer: A hypothetical heat engine, consisting of a
Chemistry 452/456
End-of-term Examination
23 August 2002
Professor G. Drobny
Useful Constants and Conversions
Universal Gas Constant= R = 8.31J / mole K = 0.0821L atm / mole K
Faradays Constant= = 96, 458 Coulombs / mole
gravitational constant=g=9.8m/s2
A
Chemistry 457 - Homework #6 Solution
due: Friday, May 9th at 5:00 pm
Readings: Chapters 15 and 16 in Engel & Reid.
Problem 1 - Equation of State. The equation of state for an atomic or molecular gas
may be determined by dierentiating the Helmholtz energy
Chemistry 457 - Homework #10 Solution
Problem 1 - Thermal Conductivity. This is a two part problem.
First, determine the ratio of the thermal conductivity for O2 at sea level ( = 0.40 nm2 ,
T = 298 K, P = 1 atm) versus the lower stratosphere (T = 230 K, P
Chem 455 Fall 2012 Homework 6 due Mon Nov 5 at 5:00pm (in box 65 on 3rd floor)
1. Oscillator. The energy eigenstates of the harmonic oscillator are described by wavefunctions that
contain the Hermite polynomials,
. Using
,
, and the recursion
relationship
Chem 455 Fall 2012 Homework 5 due Mon Oct 29 5:00pm (in box 65 on 3rd floor)
1. Tunneling. An electron with energy 0.200 eV runs into a potential step of height 3.50 eV. What is the
penetration depth of the electron?
The penetration depth is 1/K, with
. F
Chem 455 Fall 2013 Homework 9 due Mon Nov 25 5:00pm (in box 71 on 3rd floor)
1. Zeeman effect. Calculate the energy splitting, in eV, between the two 1s 2S1/2 states of a hydrogen
atom placed in an external magnetic field that is parallel to the z axis an
Chem 455 Fall 2013 Homework 8 due Mon Nov 18 5:00pm (in box 71 on 3rd floor)
1. Hydrogen atom. The energies of the stationary states of the hydrogen atom can be written in several
different ways. Starting from
(
show how to express
)(
)
as a function of t
Chem 455 Fall 2013 Homework 7 due Tue Nov 12 5:00pm (in box 71 on 3rd floor)
1. Vibration/rotation. For the molecule HD (D being deuterium, 2H), the equilibrium bond length is
74.14 pm, and the force constant is 575.0 N m-1. Use the rigid rotator-harmonic
Chem 455 Fall 2013 Homework 7 due Tue Nov 12 5:00pm (in box 71 on 3rd floor)
1. Vibration/rotation. For the molecule HD (D being deuterium, 2H), the equilibrium bond length is
74.14 pm, and the force constant is 575.0 N m-1. Use the rigid rotator-harmonic
Chem 455 Fall 2013 Homework 3 due Mon Oct 14 5:00pm (in box 71 on 3rd floor)
1. Orthonormal. Given two functions
,
determine the values for the
coefficients
and
that make the functions orthonormal over the interval
. Hint: For
an efficient solution, start